Solve for x square root of 3x+15 = square root of x+9

$\sqrt{3 x + 15} = \sqrt{x + 9}$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{3 x + 15}}^{2} = {\sqrt{x + 9}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x + 15}$ as ${(3 x + 15)}^{\frac{1}{2}}$ .

${({(3 x + 15)}^{\frac{1}{2}})}^{2} = {\sqrt{x + 9}}^{2}$

Simplify the left side.

Simplify ${({(3 x + 15)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x + 15)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(3 x + 15)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 9}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x + 15)}^{\frac{1}{2} \cdot 2} = {\sqrt{x + 9}}^{2}$

Rewrite the expression.

${(3 x + 15)}^{1} = {\sqrt{x + 9}}^{2}$

Simplify.

$3 x + 15 = {\sqrt{x + 9}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{x + 9}}^{2}$ as $x + 9$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 9}$ as ${(x + 9)}^{\frac{1}{2}}$ .

$3 x + 15 = {({(x + 9)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 x + 15 = {(x + 9)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$3 x + 15 = {(x + 9)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 x + 15 = {(x + 9)}^{\frac{2}{2}}$

Rewrite the expression.

$3 x + 15 = {(x + 9)}^{1}$

Simplify.

$3 x + 15 = x + 9$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$3 x + 15 - x = 9$

Subtract $x$ from $3 x$ .

$2 x + 15 = 9$

Move all terms not containing $x$ to the right side of the equation.

Subtract $15$ from both sides of the equation.

$2 x = 9 - 15$

Subtract $15$ from $9$ .

$2 x = - 6$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

Solve for x square root of 3x+15 = square root of x+9

Related Questions

Support LCMGCF.com by disabling your adblocker.